$A$ liquid of density $\rho$ is coming out of a hose pipe of cross-sectional area $A$ with horizontal speed $v$ and hits a mesh. $50\%$ of the liquid passes through the mesh unaffected. $25\%$ loses all of its momentum and $25\%$ comes back with the same speed. The resultant pressure on the mesh will be

An air bubble of volume $V_0$ is released by a fish at a depth $h$ in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure $P$ above the lake. The volume of the bubble just before touching the surface will be (density of water is $\rho$):

The phenomenon of lowering the freezing point of water by the application of pressure is known as

$A$ large number of droplets,each of radius $r$,coalesce to form a bigger drop of radius $R$. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. The velocity of the drop is ($T=$ surface tension,$\rho =$ density)

$A$ liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in the figure. During rotation, the liquid rises along its sides. If the radius of the vessel is $0.05 \,m$ and the speed of rotation is $10 \,rad \,s^{-1}$, then the height difference between the liquid at the centre of the vessel and its sides is $\left(g=10 \,m \,s^{-2}\right)$.

$A$ horizontal fire hose with a nozzle of cross-sectional area $\frac{5}{\sqrt{21}} \times 10^{-3} \text{ m}^2$ delivers a cubic metre of water in $10 \text{ s}$. What will be the maximum possible increase in the temperature of water while it hits a rigid wall (neglecting the effect of gravity) (in $^{\circ} \text{C}$)?